For all complex numbers $${z_1},\,{z_2}$$ satisfying $$\left| {{z_1}} \right| = 12$$ and $$\left| {{z_2} - 3 - 4i} \right| = 5,$$
the minimum value of $$\left| {{z_1} - {z_2}} \right|$$ is

The length of a longest interval in which the function $$3\,\sin x - 4{\sin ^3}x$$ is increasing, is

Which of the following pieces of data does NOT uniquely determine an acute-angled triangle $$ABC$$ ($$R$$ being the radius of the circumcircle)?

The locus of the mid-point of the line segment joining the focus to a moving point on the parabola $${y^2} = 4ax$$ is another parabola with directrix